Question: How to non-dimensionalize this 10th-degree RootOf() polynomial?

Details here: non-dimensionalization.mw. Thanks!

In short, I want to plot all the ten roots of a 10th-degree polynomial in _Z with 4 or 5 primitive parameters. To do so, I need to find that combination of parameters that allows me to transform/scale/non-dimensionalize the original polynomial in a polynomial in _Z with just (1) one parameter or at maximum (2) two parameters. In the case of (1), I can plot its roots in a standard 2D plot against the single parameter. In the case of (2), I can plot the roots in a standard 3D plot against the two parameters.

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